Human Vision
Normal human vision provides a perception of space in the visual field of view that is in color and three dimensions (3D). A better realization of the optical requirements for a photographic system to present an acceptable 3D stereoscopic image or stereo-model to the viewer is given by an understanding of stereopsis, or visual perception of space.
The stimulus conditions for space perception are termed cues, and are in two groups. The monocular group allows stereopsis with one eye and includes relative sizes of subjects, their interposition, linear and aerial perspective, distribution of light and shade, movement parallax of subject and background and visual accommodation. The binocular group uses the two coordinated activities of both eyes: firstly, visual convergence, where the optical axes converge muscularly from parallel for distant vision to a convergence angle of 23.degree. for a near point of 150 mm; and secondly, stereoscopic vision, where, due to the two different visual viewpoints, the imaging geometry gives two disparate retinal images for the left and right eyes. The disparities are due to parallax, the relative displacement of corresponding or homologous image points of a subject point away from the optical axis due to its position in the binocular field of view.
Retinal images are encoded for transmission as frequency modulated voltage impulses along the optic nerve, with signal processing taking place at the intermediate lateral geniculate bodies and then the visual cortex of the brain. The resultant visual perception is unique to the observer. For a further discussion of human 3D perception, see, e.g., Sidney F. Ray, "Applied Photographic Optics Imaging Systems For Photography, Film and Video," Focal Press, pp. 469-484, (1988), which is incorporated herein by reference.
3D Techniques
Many prior art 3D imaging systems use parallax to generate the 3D effect. Section 65.5 of Ray, cited above and which is incorporated herein by reference, provides a good description of several parallax-based techniques, such as 3D movies, stereo viewing of two side-by-side offset images, 3D post cards, etc. Although these parallax-only based systems offer some degree of 3D effect, they are discernably unrealistic.
Another well known, but far more complex technique for generating 3D images is holography. While holography can produce quite realistic 3D images, its use is quite limited because of the need for coherent light sources (such as lasers) and the darkroom or near darkroom conditions required to generate holograms.
One prior art technique for generating 3D images, known as integral photography, uses an array of small lenses (referred to as a fly's eye lens or a micro-lens array) to both generate and reproduce 3D images. The technique of integral photography is described in Ives, Herbert E., "Optical Properties of a Lippmann Lenticulated Sheet," Journal of the Optical Society of America 21(3):171-176 (1931).
Other techniques incorporating micro-lens arrays for the generation of 3D images are described in Yang et al., 1988, "Discussion of the Optics of a New 3-D Imaging System," Applied Optics 27(21):4529-4534; Davies et al., 1988, "Three-Dimensional Imaging Systems: A New Development," Applied Optics 27(21):4520-4528; Davies et al., 1994, "Design and Analysis of an Image Transfer System Using Micro-lens Arrays," Optical Engineering 33(11):3624-3633; Benton, Stephen A., 1972, "Direct Orthoscopic Stereo Panoramagram Camera," U.S. Pat. No. 3,657,981; Nims et al., 1974, "Three Dimensional Pictures and Method of Composing Them," U.S. Pat. No. 3,852,787; and Davies et al., 1991, "Imaging System," U.S. Pat. No. 5,040,871, each of which is incorporated herein by reference. A drawback of the above micro-lens array based 3D optical systems is that all lenses in the array have a fixed focal length. This greatly limits the type of 3D effects that can be generated by such arrays.
The Fabrication of Micro-Lens Arrays
Great advances in the generation of very small scale surface features have been made recently. Micro-stamping techniques using self assembling monolayers (SAMs) have allowed low cost production of features on sub-micron (&lt;10.sup.-6 m) scales.
Certain compounds, when placed in an appropriate environment, are capable of spontaneously forming an ordered two dimensional crystalline array. For example, solutions of alkane thiols exhibit this property on gold. Micro-stamping or micro contact printing uses a `rubber` (silicone elastomer) stamp to selectively deposit alkane thiols in small domains on gold surfaces. A `master` mold with the desired feature shapes and sizes is fabricated using optical lithographic techniques well known in the electronic arts. Poly(dimethylsiloxane) (PDMS), a silicone elastomer, is poured over the master and allowed to cure and then gently removed. The resulting stamp is then inked by brushing the PDMS surface with a solution of the appropriate alkane thiol. The PDMS stamp is then placed on a gold surface and the desired pattern of alkane thiols is deposited selectively as a monolayer on the surface. The monolayers may be derivatized with various head groups (exposed to the environment away from the metallic surface) in order to tailor the properties of the surface.
In this fashion, alternating domains, hydrophilic and hydrophobic, may be easily fabricated on a surface on a very small scale. Under appropriate conditions, such a surface, when cooled in the presence of water vapor, will selectively condense water droplets on the hydrophilic surface domains. Such droplets can act as convergent or divergent micro-lenses. Any shape lens or lens element may be produced. SAMs may be selectively deposited on planar or curved surfaces which may or may not be optically transparent. Offsetting, adjacent, stacked, and other configurations of SAM surfaces may all be used to generate complex lens shapes.
Using techniques similar to the SAM techniques discussed above, transparent polymers have been used to make stable micro-lenses. For example, a solution of unpolymerized monomers (which are hydrophilic) will selectively adsorb to hydrophilic domains on a derivatized SAM surface. At that point, polymerization may be initiated (e.g., by heating). By varying the shape of the derivatized surface domains, the amount of solution on the domain, and the solution composition, a great variety of different lenses with different optical properties may be formed.
For examples of optical techniques incorporating liquid optical elements and SAMs, see Kumar et al., 1994, "Patterned Condensation Figures as Optical Diffraction Gratings," Science 263:60-62; Kumar et al., 1993, "Features of Gold Having Micrometer to Centimeter Dimensions Can be Formed Through a Combination of Stamping With an Elastomeric Stamp and an Alkanethiol `Ink` Followed by Chemical Etching," Appl. Phys. Lett. 63(14):2002-2004; Kumar et al., 1994, "Patterning Self-Assembled Monolayers: Applications in Materials Science," Langmuir 10(5):1498-1511; Chaudhury et al., 1992, "How to Make Water Run Uphill," Science 256:1539-1541; Abbott et al., 1994, "Potential-Dependent Wetting of Aqueous Solutions on Self-Assembled Monolayers Formed From 15-(Ferrocenylcarbonyl)pentadecanethiol on Gold," Langmuir 10(5):1493-1497; and Gorman et al., in press, "Control of the Shape of Liquid Lenses on a Modified Gold Surface Using an Applied Electrical Potential Across a Self-Assembled Monolayer," Harvard University, Department of Chemistry, each of which is incorporated herein by reference.
Micro-lens arrays can also be fabricated using several other well known techniques. Some illustrative techniques for the generation of micro-lens or micromirror arrays are disclosed in the following articles, each of which is incorporated herein by reference: Liau et al., 1994, "Large-Numerical-Aperture Micro-lens Fabrication by One-Step Etching and Mass-Transport Smoothing," Appl. Phys. Lett. 64(12):1484-1486; Jay et al., 1994, "Preshaping Photoresist for Refractive Micro-lens Fabrication," Optical Engineering 33(11):3552-3555; MacFarlane et al., 1994, "Microjet Fabrication of Micro-lens Arrays," IEEE Photonics Technology Letters 6(9):1112-1114; Stern et al., 1994, "Dry Etching for Coherent Refractive Micro-lens Arrays," Optical Engineering 33(11):3547-3551; and Kendall et al., 1994, "Micromirror Arrays Using KOH:H.sub.2 O Micromachining of Silicon for Lens Templates, Geodesic Lenses, and Other Applications," Optical Engineering 33(11):3578-3588.
Focal Length Variation and Control
Using the micro-stamping technique discussed above, small lenses may be fabricated with variable focal lengths. Variable focus may be achieved through several general means, e.g., (i) through the use of electrical potentials; (ii) through mechanical deformation; (iii) through selective deposition, such as deposition of liquid water drops from the vapor phase (as described in Kumar et al., (Science, 1994) cited above); and (iv) heating or melting (e.g., structures may be melted to change optical properties, as in some micro-lens arrays which are crudely molded and then melted into finer optical elements).
The degree to which a solution wets or spreads on a surface may be controlled by varying the electronic properties of the system. For example, by placing microelectrodes within the liquid lens and varying the potential with respect to the surface, the curvature of the lens may be varied. See Abbott et al, cited above. In other configurations, hydrophobic liquid micro-lenses are formed on a surface and covered with an aqueous solution and the surface potential is varied versus the aqueous solution. Such systems have demonstrated extremely small volume lenses (1nL) which are capable of reversibly and rapidly varying focus (see Gorman et al., cited above).
Referring now to FIGS. 3(a)-3(c), schematic diagrams of a variable focus lens 50 is shown. Variable focus lens 50 includes a liquid lens 52 and two SAM surfaces 54. SAM surfaces 54 adhere to liquid lens 52. As can be seen in the progression from FIGS. 3(a) through 3(c), by varying the distance between the SAM surfaces 54, the shape, and therefore optical characteristics, of liquid lens 52 can be altered. There are also several other ways to vary the shape and optical characteristics of liquid lens 52. For example, the electrical potential between lens 52 and surface 54 can be varied, causing changes in the shape of lens 52, as is discussed further below with respect to FIGS. 4(a)-4(c). The index of refraction of lens 52 can be varied by using different liquid materials. The cohesive and adhesive properties of liquid lens 52 can be adjusted by varying the chemistry of the liquid material, and by varying the chemistry of surface 54. The three dimensional characteristics of surface 54 can be varied. For example, when viewed from the top or bottom surface 54 can be circular, rectangular, hexagonal, or any other shape, and may be moved up and down. These techniques may be used individually or in combination to create a variety of lens shapes and optical effects.
Referring now to FIGS. 4(a)-4(c), a schematic diagrams of an electrically variable focus lens as disclosed in the above cited Abbott et al. article is shown. A drop of liquid 52 is placed on SAM surface 54, which is in turn formed on metallic surface 56, preferably gold. By varying the electric potential between microelectrode 58 and SAM surface 54, the curvature (and thus optical characteristics) of liquid lens 52 can be varied. The progression from FIGS. 4(a) to 4(c) shows schematically how the shape of liquid lens 52 can be changed. Similar effects can be achieved using the techniques described in the above Gorman et al. article, although microelectrodes 58 need not be used.
Alternatively, such micro-lenses may be focused through mechanical means. For example, flexible polymeric or elastomeric lenses may be compressed or relaxed so as to vary 30 focus through piezoelectric means. Alternatively, liquid lenses encapsulated in flexible casings may be mechanically compressed or relaxed.